TSTP Solution File: RNG103+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG103+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:57:54 EDT 2023
% Result : Theorem 13.15s 2.60s
% Output : Proof 18.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG103+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:05:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.88/1.16 Prover 4: Preprocessing ...
% 2.88/1.16 Prover 1: Preprocessing ...
% 3.52/1.20 Prover 0: Preprocessing ...
% 3.52/1.20 Prover 6: Preprocessing ...
% 3.52/1.20 Prover 2: Preprocessing ...
% 3.52/1.20 Prover 3: Preprocessing ...
% 3.52/1.20 Prover 5: Preprocessing ...
% 9.30/2.04 Prover 1: Constructing countermodel ...
% 9.59/2.11 Prover 6: Proving ...
% 9.59/2.11 Prover 5: Proving ...
% 9.59/2.12 Prover 3: Constructing countermodel ...
% 9.59/2.23 Prover 2: Proving ...
% 11.44/2.32 Prover 4: Constructing countermodel ...
% 11.91/2.41 Prover 0: Proving ...
% 13.15/2.60 Prover 3: proved (1977ms)
% 13.15/2.60
% 13.15/2.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.15/2.60
% 13.15/2.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.15/2.60 Prover 0: stopped
% 13.15/2.60 Prover 2: stopped
% 13.15/2.60 Prover 6: stopped
% 13.72/2.62 Prover 5: stopped
% 13.72/2.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.72/2.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.72/2.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.72/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.14/2.74 Prover 11: Preprocessing ...
% 14.14/2.75 Prover 13: Preprocessing ...
% 14.79/2.76 Prover 7: Preprocessing ...
% 14.79/2.77 Prover 8: Preprocessing ...
% 14.79/2.77 Prover 10: Preprocessing ...
% 15.78/2.94 Prover 10: Constructing countermodel ...
% 16.09/2.95 Prover 7: Constructing countermodel ...
% 16.09/3.01 Prover 8: Warning: ignoring some quantifiers
% 16.09/3.02 Prover 8: Constructing countermodel ...
% 16.65/3.04 Prover 13: Warning: ignoring some quantifiers
% 16.65/3.07 Prover 13: Constructing countermodel ...
% 17.84/3.19 Prover 10: Found proof (size 15)
% 17.84/3.19 Prover 10: proved (552ms)
% 17.84/3.19 Prover 11: Constructing countermodel ...
% 17.84/3.19 Prover 7: stopped
% 17.84/3.19 Prover 8: stopped
% 17.84/3.19 Prover 1: stopped
% 17.84/3.19 Prover 13: stopped
% 17.84/3.19 Prover 4: stopped
% 17.84/3.20 Prover 11: stopped
% 17.84/3.20
% 17.84/3.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.84/3.20
% 17.84/3.20 % SZS output start Proof for theBenchmark
% 17.84/3.21 Assumptions after simplification:
% 17.84/3.21 ---------------------------------
% 17.84/3.21
% 17.84/3.21 (mAMDistr)
% 18.10/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.10/3.23 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 18.10/3.23 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.10/3.23 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7:
% 18.10/3.23 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2,
% 18.10/3.23 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8,
% 18.10/3.23 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 18.10/3.23 $i(v5)))
% 18.10/3.23
% 18.10/3.23 (m__)
% 18.10/3.24 $i(xv) & $i(xu) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ?
% 18.10/3.24 [v2: $i] : ( ~ (v2 = v0) & sdtasdt0(xc, v1) = v2 & sdtpldt0(xu, xv) = v1 &
% 18.10/3.24 sdtpldt0(xx, xy) = v0 & $i(v2) & $i(v1) & $i(v0))
% 18.10/3.24
% 18.10/3.24 (m__1905)
% 18.10/3.24 $i(xc) & aElement0(xc)
% 18.10/3.24
% 18.10/3.24 (m__1956)
% 18.10/3.24 sdtasdt0(xc, xu) = xx & $i(xu) & $i(xx) & $i(xc) & aElement0(xu)
% 18.10/3.24
% 18.10/3.24 (m__1979)
% 18.10/3.24 sdtasdt0(xc, xv) = xy & $i(xv) & $i(xy) & $i(xc) & aElement0(xv)
% 18.10/3.24
% 18.10/3.24 (function-axioms)
% 18.10/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.20/3.24 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.20/3.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 18.20/3.24 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.20/3.24 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 18.20/3.24 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.20/3.24 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.20/3.24 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 18.20/3.24 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.20/3.24 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.20/3.24 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 18.20/3.24
% 18.20/3.24 Further assumptions not needed in the proof:
% 18.20/3.24 --------------------------------------------
% 18.20/3.24 mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv,
% 18.20/3.24 mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, mDefSSum,
% 18.20/3.24 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm,
% 18.20/3.24 mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, mSetSort, mSortsB,
% 18.20/3.24 mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__1933
% 18.20/3.24
% 18.20/3.24 Those formulas are unsatisfiable:
% 18.20/3.24 ---------------------------------
% 18.20/3.24
% 18.20/3.24 Begin of proof
% 18.20/3.24 |
% 18.20/3.24 | ALPHA: (m__1905) implies:
% 18.20/3.24 | (1) aElement0(xc)
% 18.20/3.24 |
% 18.20/3.24 | ALPHA: (m__1956) implies:
% 18.20/3.25 | (2) aElement0(xu)
% 18.20/3.25 | (3) sdtasdt0(xc, xu) = xx
% 18.20/3.25 |
% 18.20/3.25 | ALPHA: (m__1979) implies:
% 18.20/3.25 | (4) aElement0(xv)
% 18.20/3.25 | (5) sdtasdt0(xc, xv) = xy
% 18.20/3.25 |
% 18.20/3.25 | ALPHA: (m__) implies:
% 18.20/3.25 | (6) $i(xc)
% 18.20/3.25 | (7) $i(xu)
% 18.20/3.25 | (8) $i(xv)
% 18.20/3.25 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & sdtasdt0(xc,
% 18.20/3.25 | v1) = v2 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 & $i(v2) &
% 18.20/3.25 | $i(v1) & $i(v0))
% 18.20/3.25 |
% 18.20/3.25 | ALPHA: (function-axioms) implies:
% 18.20/3.25 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.20/3.25 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 18.20/3.25 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.20/3.25 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 18.20/3.25 |
% 18.20/3.25 | DELTA: instantiating (9) with fresh symbols all_33_0, all_33_1, all_33_2
% 18.20/3.25 | gives:
% 18.20/3.25 | (12) ~ (all_33_0 = all_33_2) & sdtasdt0(xc, all_33_1) = all_33_0 &
% 18.20/3.25 | sdtpldt0(xu, xv) = all_33_1 & sdtpldt0(xx, xy) = all_33_2 &
% 18.20/3.25 | $i(all_33_0) & $i(all_33_1) & $i(all_33_2)
% 18.20/3.25 |
% 18.20/3.25 | ALPHA: (12) implies:
% 18.20/3.25 | (13) ~ (all_33_0 = all_33_2)
% 18.20/3.25 | (14) sdtpldt0(xx, xy) = all_33_2
% 18.20/3.25 | (15) sdtpldt0(xu, xv) = all_33_1
% 18.20/3.25 | (16) sdtasdt0(xc, all_33_1) = all_33_0
% 18.20/3.25 |
% 18.20/3.25 | GROUND_INST: instantiating (mAMDistr) with xc, xu, xv, xx, xy, all_33_2,
% 18.20/3.25 | simplifying with (1), (2), (3), (4), (5), (6), (7), (8), (14)
% 18.20/3.25 | gives:
% 18.20/3.25 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0,
% 18.20/3.25 | xc) = v1 & sdtasdt0(xv, xc) = v3 & sdtasdt0(xu, xc) = v2 &
% 18.20/3.25 | sdtasdt0(xc, v0) = all_33_2 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu,
% 18.20/3.25 | xv) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_33_2))
% 18.20/3.25 |
% 18.20/3.25 | DELTA: instantiating (17) with fresh symbols all_54_0, all_54_1, all_54_2,
% 18.20/3.25 | all_54_3 gives:
% 18.20/3.26 | (18) sdtasdt0(all_54_3, xc) = all_54_2 & sdtasdt0(xv, xc) = all_54_0 &
% 18.20/3.26 | sdtasdt0(xu, xc) = all_54_1 & sdtasdt0(xc, all_54_3) = all_33_2 &
% 18.20/3.26 | sdtpldt0(all_54_1, all_54_0) = all_54_2 & sdtpldt0(xu, xv) = all_54_3
% 18.20/3.26 | & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3) &
% 18.20/3.26 | $i(all_33_2)
% 18.20/3.26 |
% 18.20/3.26 | ALPHA: (18) implies:
% 18.20/3.26 | (19) sdtpldt0(xu, xv) = all_54_3
% 18.20/3.26 | (20) sdtasdt0(xc, all_54_3) = all_33_2
% 18.20/3.26 |
% 18.20/3.26 | GROUND_INST: instantiating (10) with all_33_1, all_54_3, xv, xu, simplifying
% 18.20/3.26 | with (15), (19) gives:
% 18.20/3.26 | (21) all_54_3 = all_33_1
% 18.20/3.26 |
% 18.20/3.26 | REDUCE: (20), (21) imply:
% 18.20/3.26 | (22) sdtasdt0(xc, all_33_1) = all_33_2
% 18.20/3.26 |
% 18.20/3.26 | GROUND_INST: instantiating (11) with all_33_0, all_33_2, all_33_1, xc,
% 18.20/3.26 | simplifying with (16), (22) gives:
% 18.20/3.26 | (23) all_33_0 = all_33_2
% 18.20/3.26 |
% 18.20/3.26 | REDUCE: (13), (23) imply:
% 18.20/3.26 | (24) $false
% 18.20/3.26 |
% 18.20/3.26 | CLOSE: (24) is inconsistent.
% 18.20/3.26 |
% 18.20/3.26 End of proof
% 18.20/3.26 % SZS output end Proof for theBenchmark
% 18.20/3.26
% 18.20/3.26 2656ms
%------------------------------------------------------------------------------